A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems. (1st February 2017)

• Record Type: Journal Article
• Authors: Qin, Fangfang; Chen, Jinru; Li, Zhilin; Cai, Mingchao
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 3(2017)
• Page Start: 404
• Page End: 418
• Publication Date: 2017-02-01
• Subjects: Nonconforming immersed finite element -- Elasticity interface problems -- Cartesian grid; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.11.033
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, a new nonconforming immersed finite element (IFE) method on triangular Cartesian meshes is developed for solving planar elasticity interface problems. The proposed IFE method possesses optimal approximation property for both compressible and nearly incompressible problems. Its degree of freedom is much less than those of existing finite element methods for the same problem. Moreover, the method is robust with respect to the shape of the interface and its location relative to the domain and the underlying mesh. Both theory and numerical experiments are presented to demonstrate the effectiveness of the new method. Theoretically, the unisolvent property and the consistency of the IFE space are proved. Experimentally, extensive numerical examples are given to show that the approximation orders in L 2 norm and semi- H 1 norm are optimal under various Lamé parameters settings and different interface geometry configurations.